Question

 A sequence is bounded if and only if it is both bounded above and bounded

below.

Answer 1

Let $x_n$ be a bounded sequence. $\iff |x_n| \leq K , K\in \mathbb{R} ~ \forall n \in \mathbb{N}$

$\iff -K \leq x_n \leq K$

$\iff x_n$ is both bounded above and bounded below.